Properties

Label 726.2.e.b.565.1
Level $726$
Weight $2$
Character 726.565
Analytic conductor $5.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.e (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.79713918674\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 565.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 726.565
Dual form 726.2.e.b.487.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(-0.618034 + 1.90211i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-4.85410 + 3.52671i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.23607 - 3.80423i) q^{19} -2.00000 q^{21} +6.00000 q^{23} +(-0.809017 - 0.587785i) q^{24} +(-1.54508 + 4.75528i) q^{25} +(1.23607 + 3.80423i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.61803 - 1.17557i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-6.47214 - 4.70228i) q^{31} +1.00000 q^{32} +6.00000 q^{34} +(0.309017 - 0.951057i) q^{36} +(-3.09017 - 9.51057i) q^{37} +(-3.23607 + 2.35114i) q^{38} +(-3.23607 + 2.35114i) q^{39} +(-1.85410 + 5.70634i) q^{41} +(1.61803 + 1.17557i) q^{42} -8.00000 q^{43} +(-4.85410 - 3.52671i) q^{46} +(-1.85410 + 5.70634i) q^{47} +(0.309017 + 0.951057i) q^{48} +(2.42705 - 1.76336i) q^{49} +(4.04508 - 2.93893i) q^{50} +(1.85410 + 5.70634i) q^{51} +(1.23607 - 3.80423i) q^{52} +1.00000 q^{54} -2.00000 q^{56} +(-3.23607 - 2.35114i) q^{57} +(-1.85410 + 5.70634i) q^{58} +(6.47214 - 4.70228i) q^{61} +(2.47214 + 7.60845i) q^{62} +(-0.618034 + 1.90211i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.00000 q^{67} +(-4.85410 - 3.52671i) q^{68} +(1.85410 - 5.70634i) q^{69} +(-4.85410 + 3.52671i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-0.618034 - 1.90211i) q^{73} +(-3.09017 + 9.51057i) q^{74} +(4.04508 + 2.93893i) q^{75} +4.00000 q^{76} +4.00000 q^{78} +(11.3262 + 8.22899i) q^{79} +(0.309017 + 0.951057i) q^{81} +(4.85410 - 3.52671i) q^{82} +(-9.70820 + 7.05342i) q^{83} +(-0.618034 - 1.90211i) q^{84} +(6.47214 + 4.70228i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(-2.47214 + 7.60845i) q^{91} +(1.85410 + 5.70634i) q^{92} +(-6.47214 + 4.70228i) q^{93} +(4.85410 - 3.52671i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-11.3262 - 8.22899i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9} + 4 q^{12} - 4 q^{13} + 2 q^{14} - q^{16} - 6 q^{17} - q^{18} - 4 q^{19} - 8 q^{21} + 24 q^{23} - q^{24} + 5 q^{25} - 4 q^{26} - q^{27} + 2 q^{28} + 6 q^{29} - 8 q^{31} + 4 q^{32} + 24 q^{34} - q^{36} + 10 q^{37} - 4 q^{38} - 4 q^{39} + 6 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} + 5 q^{50} - 6 q^{51} - 4 q^{52} + 4 q^{54} - 8 q^{56} - 4 q^{57} + 6 q^{58} + 8 q^{61} - 8 q^{62} + 2 q^{63} - q^{64} - 16 q^{67} - 6 q^{68} - 6 q^{69} - 6 q^{71} - q^{72} + 2 q^{73} + 10 q^{74} + 5 q^{75} + 16 q^{76} + 16 q^{78} + 14 q^{79} - q^{81} + 6 q^{82} - 12 q^{83} + 2 q^{84} + 8 q^{86} - 24 q^{87} - 24 q^{89} + 8 q^{91} - 6 q^{92} - 8 q^{93} + 6 q^{94} - q^{96} - 14 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(607\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 0.587785i −0.572061 0.415627i
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(6\) −0.809017 + 0.587785i −0.330280 + 0.239962i
\(7\) −0.618034 1.90211i −0.233595 0.718931i −0.997305 0.0733714i \(-0.976624\pi\)
0.763710 0.645560i \(-0.223376\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) −3.23607 2.35114i −0.897524 0.652089i 0.0403050 0.999187i \(-0.487167\pi\)
−0.937829 + 0.347098i \(0.887167\pi\)
\(14\) −0.618034 + 1.90211i −0.165177 + 0.508361i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −4.85410 + 3.52671i −1.17729 + 0.855353i −0.991864 0.127304i \(-0.959367\pi\)
−0.185429 + 0.982658i \(0.559367\pi\)
\(18\) 0.309017 + 0.951057i 0.0728360 + 0.224166i
\(19\) 1.23607 3.80423i 0.283573 0.872749i −0.703249 0.710943i \(-0.748268\pi\)
0.986823 0.161806i \(-0.0517318\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −0.809017 0.587785i −0.165140 0.119981i
\(25\) −1.54508 + 4.75528i −0.309017 + 0.951057i
\(26\) 1.23607 + 3.80423i 0.242413 + 0.746070i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 1.61803 1.17557i 0.305780 0.222162i
\(29\) −1.85410 5.70634i −0.344298 1.05964i −0.961958 0.273196i \(-0.911919\pi\)
0.617660 0.786445i \(-0.288081\pi\)
\(30\) 0 0
\(31\) −6.47214 4.70228i −1.16243 0.844555i −0.172347 0.985036i \(-0.555135\pi\)
−0.990083 + 0.140482i \(0.955135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0.309017 0.951057i 0.0515028 0.158509i
\(37\) −3.09017 9.51057i −0.508021 1.56353i −0.795632 0.605780i \(-0.792861\pi\)
0.287611 0.957747i \(-0.407139\pi\)
\(38\) −3.23607 + 2.35114i −0.524960 + 0.381405i
\(39\) −3.23607 + 2.35114i −0.518186 + 0.376484i
\(40\) 0 0
\(41\) −1.85410 + 5.70634i −0.289562 + 0.891180i 0.695432 + 0.718592i \(0.255213\pi\)
−0.984994 + 0.172588i \(0.944787\pi\)
\(42\) 1.61803 + 1.17557i 0.249668 + 0.181394i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −4.85410 3.52671i −0.715698 0.519985i
\(47\) −1.85410 + 5.70634i −0.270449 + 0.832355i 0.719939 + 0.694037i \(0.244170\pi\)
−0.990388 + 0.138318i \(0.955830\pi\)
\(48\) 0.309017 + 0.951057i 0.0446028 + 0.137273i
\(49\) 2.42705 1.76336i 0.346722 0.251908i
\(50\) 4.04508 2.93893i 0.572061 0.415627i
\(51\) 1.85410 + 5.70634i 0.259626 + 0.799047i
\(52\) 1.23607 3.80423i 0.171412 0.527551i
\(53\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −3.23607 2.35114i −0.428628 0.311416i
\(58\) −1.85410 + 5.70634i −0.243456 + 0.749279i
\(59\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(60\) 0 0
\(61\) 6.47214 4.70228i 0.828672 0.602066i −0.0905112 0.995895i \(-0.528850\pi\)
0.919183 + 0.393830i \(0.128850\pi\)
\(62\) 2.47214 + 7.60845i 0.313962 + 0.966274i
\(63\) −0.618034 + 1.90211i −0.0778650 + 0.239644i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −4.85410 3.52671i −0.588646 0.427677i
\(69\) 1.85410 5.70634i 0.223208 0.686963i
\(70\) 0 0
\(71\) −4.85410 + 3.52671i −0.576076 + 0.418544i −0.837307 0.546733i \(-0.815871\pi\)
0.261231 + 0.965276i \(0.415871\pi\)
\(72\) −0.809017 + 0.587785i −0.0953436 + 0.0692712i
\(73\) −0.618034 1.90211i −0.0723354 0.222625i 0.908352 0.418206i \(-0.137341\pi\)
−0.980688 + 0.195580i \(0.937341\pi\)
\(74\) −3.09017 + 9.51057i −0.359225 + 1.10558i
\(75\) 4.04508 + 2.93893i 0.467086 + 0.339358i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 11.3262 + 8.22899i 1.27430 + 0.925834i 0.999365 0.0356284i \(-0.0113433\pi\)
0.274936 + 0.961462i \(0.411343\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 4.85410 3.52671i 0.536046 0.389460i
\(83\) −9.70820 + 7.05342i −1.06561 + 0.774214i −0.975119 0.221683i \(-0.928845\pi\)
−0.0904951 + 0.995897i \(0.528845\pi\)
\(84\) −0.618034 1.90211i −0.0674330 0.207538i
\(85\) 0 0
\(86\) 6.47214 + 4.70228i 0.697908 + 0.507060i
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −2.47214 + 7.60845i −0.259150 + 0.797582i
\(92\) 1.85410 + 5.70634i 0.193303 + 0.594927i
\(93\) −6.47214 + 4.70228i −0.671129 + 0.487604i
\(94\) 4.85410 3.52671i 0.500662 0.363753i
\(95\) 0 0
\(96\) 0.309017 0.951057i 0.0315389 0.0970668i
\(97\) −11.3262 8.22899i −1.15001 0.835528i −0.161524 0.986869i \(-0.551641\pi\)
−0.988482 + 0.151341i \(0.951641\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 4.85410 + 3.52671i 0.483001 + 0.350921i 0.802486 0.596670i \(-0.203510\pi\)
−0.319485 + 0.947591i \(0.603510\pi\)
\(102\) 1.85410 5.70634i 0.183583 0.565012i
\(103\) −1.23607 3.80423i −0.121793 0.374842i 0.871510 0.490378i \(-0.163141\pi\)
−0.993303 + 0.115536i \(0.963141\pi\)
\(104\) −3.23607 + 2.35114i −0.317323 + 0.230548i
\(105\) 0 0
\(106\) 0 0
\(107\) 3.70820 11.4127i 0.358486 1.10331i −0.595475 0.803374i \(-0.703036\pi\)
0.953961 0.299932i \(-0.0969638\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 1.61803 + 1.17557i 0.152890 + 0.111081i
\(113\) 5.56231 17.1190i 0.523258 1.61042i −0.244478 0.969655i \(-0.578617\pi\)
0.767736 0.640767i \(-0.221383\pi\)
\(114\) 1.23607 + 3.80423i 0.115768 + 0.356298i
\(115\) 0 0
\(116\) 4.85410 3.52671i 0.450692 0.327447i
\(117\) 1.23607 + 3.80423i 0.114275 + 0.351701i
\(118\) 0 0
\(119\) 9.70820 + 7.05342i 0.889950 + 0.646586i
\(120\) 0 0
\(121\) 0 0
\(122\) −8.00000 −0.724286
\(123\) 4.85410 + 3.52671i 0.437680 + 0.317993i
\(124\) 2.47214 7.60845i 0.222004 0.683259i
\(125\) 0 0
\(126\) 1.61803 1.17557i 0.144146 0.104728i
\(127\) 11.3262 8.22899i 1.00504 0.730205i 0.0418779 0.999123i \(-0.486666\pi\)
0.963163 + 0.268918i \(0.0866659\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) −2.47214 + 7.60845i −0.217659 + 0.669887i
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 3.23607 + 2.35114i 0.279554 + 0.203108i
\(135\) 0 0
\(136\) 1.85410 + 5.70634i 0.158988 + 0.489315i
\(137\) 14.5623 10.5801i 1.24414 0.903922i 0.246275 0.969200i \(-0.420793\pi\)
0.997867 + 0.0652782i \(0.0207935\pi\)
\(138\) −4.85410 + 3.52671i −0.413209 + 0.300214i
\(139\) 1.23607 + 3.80423i 0.104842 + 0.322670i 0.989693 0.143203i \(-0.0457402\pi\)
−0.884851 + 0.465873i \(0.845740\pi\)
\(140\) 0 0
\(141\) 4.85410 + 3.52671i 0.408789 + 0.297003i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −0.618034 + 1.90211i −0.0511489 + 0.157420i
\(147\) −0.927051 2.85317i −0.0764619 0.235325i
\(148\) 8.09017 5.87785i 0.665008 0.483157i
\(149\) −4.85410 + 3.52671i −0.397664 + 0.288919i −0.768589 0.639743i \(-0.779041\pi\)
0.370925 + 0.928663i \(0.379041\pi\)
\(150\) −1.54508 4.75528i −0.126156 0.388267i
\(151\) 3.09017 9.51057i 0.251474 0.773959i −0.743029 0.669259i \(-0.766612\pi\)
0.994504 0.104700i \(-0.0333882\pi\)
\(152\) −3.23607 2.35114i −0.262480 0.190703i
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −3.23607 2.35114i −0.259093 0.188242i
\(157\) 0.618034 1.90211i 0.0493245 0.151805i −0.923361 0.383934i \(-0.874569\pi\)
0.972685 + 0.232129i \(0.0745691\pi\)
\(158\) −4.32624 13.3148i −0.344177 1.05927i
\(159\) 0 0
\(160\) 0 0
\(161\) −3.70820 11.4127i −0.292247 0.899445i
\(162\) 0.309017 0.951057i 0.0242787 0.0747221i
\(163\) 3.23607 + 2.35114i 0.253468 + 0.184156i 0.707263 0.706951i \(-0.249930\pi\)
−0.453794 + 0.891107i \(0.649930\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 9.70820 + 7.05342i 0.751243 + 0.545810i 0.896212 0.443626i \(-0.146308\pi\)
−0.144969 + 0.989436i \(0.546308\pi\)
\(168\) −0.618034 + 1.90211i −0.0476824 + 0.146751i
\(169\) 0.927051 + 2.85317i 0.0713116 + 0.219475i
\(170\) 0 0
\(171\) −3.23607 + 2.35114i −0.247468 + 0.179796i
\(172\) −2.47214 7.60845i −0.188499 0.580139i
\(173\) −1.85410 + 5.70634i −0.140965 + 0.433845i −0.996470 0.0839492i \(-0.973247\pi\)
0.855505 + 0.517794i \(0.173247\pi\)
\(174\) 4.85410 + 3.52671i 0.367989 + 0.267359i
\(175\) 10.0000 0.755929
\(176\) 0 0
\(177\) 0 0
\(178\) 4.85410 + 3.52671i 0.363830 + 0.264338i
\(179\) 7.41641 22.8254i 0.554328 1.70605i −0.143382 0.989667i \(-0.545798\pi\)
0.697710 0.716380i \(-0.254202\pi\)
\(180\) 0 0
\(181\) 17.7984 12.9313i 1.32294 0.961174i 0.323052 0.946381i \(-0.395291\pi\)
0.999891 0.0147930i \(-0.00470892\pi\)
\(182\) 6.47214 4.70228i 0.479747 0.348556i
\(183\) −2.47214 7.60845i −0.182746 0.562433i
\(184\) 1.85410 5.70634i 0.136686 0.420677i
\(185\) 0 0
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 1.61803 + 1.17557i 0.117695 + 0.0855102i
\(190\) 0 0
\(191\) 5.56231 + 17.1190i 0.402474 + 1.23869i 0.922986 + 0.384834i \(0.125741\pi\)
−0.520511 + 0.853855i \(0.674259\pi\)
\(192\) −0.809017 + 0.587785i −0.0583858 + 0.0424197i
\(193\) 11.3262 8.22899i 0.815280 0.592336i −0.100076 0.994980i \(-0.531909\pi\)
0.915357 + 0.402644i \(0.131909\pi\)
\(194\) 4.32624 + 13.3148i 0.310606 + 0.955946i
\(195\) 0 0
\(196\) 2.42705 + 1.76336i 0.173361 + 0.125954i
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 4.04508 + 2.93893i 0.286031 + 0.207813i
\(201\) −1.23607 + 3.80423i −0.0871855 + 0.268329i
\(202\) −1.85410 5.70634i −0.130454 0.401497i
\(203\) −9.70820 + 7.05342i −0.681382 + 0.495053i
\(204\) −4.85410 + 3.52671i −0.339855 + 0.246919i
\(205\) 0 0
\(206\) −1.23607 + 3.80423i −0.0861209 + 0.265053i
\(207\) −4.85410 3.52671i −0.337383 0.245123i
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) 6.47214 + 4.70228i 0.445560 + 0.323718i 0.787840 0.615880i \(-0.211199\pi\)
−0.342280 + 0.939598i \(0.611199\pi\)
\(212\) 0 0
\(213\) 1.85410 + 5.70634i 0.127041 + 0.390992i
\(214\) −9.70820 + 7.05342i −0.663639 + 0.482162i
\(215\) 0 0
\(216\) 0.309017 + 0.951057i 0.0210259 + 0.0647112i
\(217\) −4.94427 + 15.2169i −0.335639 + 1.03299i
\(218\) −3.23607 2.35114i −0.219174 0.159239i
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 8.09017 + 5.87785i 0.542977 + 0.394496i
\(223\) −4.94427 + 15.2169i −0.331093 + 1.01900i 0.637522 + 0.770432i \(0.279960\pi\)
−0.968615 + 0.248567i \(0.920040\pi\)
\(224\) −0.618034 1.90211i −0.0412941 0.127090i
\(225\) 4.04508 2.93893i 0.269672 0.195928i
\(226\) −14.5623 + 10.5801i −0.968670 + 0.703780i
\(227\) 3.70820 + 11.4127i 0.246122 + 0.757486i 0.995450 + 0.0952867i \(0.0303768\pi\)
−0.749328 + 0.662199i \(0.769623\pi\)
\(228\) 1.23607 3.80423i 0.0818606 0.251941i
\(229\) 17.7984 + 12.9313i 1.17615 + 0.854523i 0.991732 0.128325i \(-0.0409601\pi\)
0.184418 + 0.982848i \(0.440960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −14.5623 10.5801i −0.954008 0.693128i −0.00225687 0.999997i \(-0.500718\pi\)
−0.951752 + 0.306870i \(0.900718\pi\)
\(234\) 1.23607 3.80423i 0.0808043 0.248690i
\(235\) 0 0
\(236\) 0 0
\(237\) 11.3262 8.22899i 0.735718 0.534531i
\(238\) −3.70820 11.4127i −0.240367 0.739774i
\(239\) 3.70820 11.4127i 0.239864 0.738225i −0.756575 0.653907i \(-0.773129\pi\)
0.996439 0.0843180i \(-0.0268712\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 6.47214 + 4.70228i 0.414336 + 0.301033i
\(245\) 0 0
\(246\) −1.85410 5.70634i −0.118213 0.363823i
\(247\) −12.9443 + 9.40456i −0.823624 + 0.598398i
\(248\) −6.47214 + 4.70228i −0.410981 + 0.298595i
\(249\) 3.70820 + 11.4127i 0.234998 + 0.723249i
\(250\) 0 0
\(251\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −9.27051 28.5317i −0.578279 1.77976i −0.624734 0.780838i \(-0.714792\pi\)
0.0464552 0.998920i \(-0.485208\pi\)
\(258\) 6.47214 4.70228i 0.402938 0.292751i
\(259\) −16.1803 + 11.7557i −1.00540 + 0.730464i
\(260\) 0 0
\(261\) −1.85410 + 5.70634i −0.114766 + 0.353214i
\(262\) −9.70820 7.05342i −0.599775 0.435762i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6.47214 + 4.70228i 0.396832 + 0.288315i
\(267\) −1.85410 + 5.70634i −0.113469 + 0.349222i
\(268\) −1.23607 3.80423i −0.0755049 0.232380i
\(269\) 19.4164 14.1068i 1.18384 0.860110i 0.191240 0.981543i \(-0.438749\pi\)
0.992600 + 0.121434i \(0.0387492\pi\)
\(270\) 0 0
\(271\) −0.618034 1.90211i −0.0375429 0.115545i 0.930529 0.366219i \(-0.119348\pi\)
−0.968072 + 0.250674i \(0.919348\pi\)
\(272\) 1.85410 5.70634i 0.112421 0.345998i
\(273\) 6.47214 + 4.70228i 0.391711 + 0.284595i
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) −12.9443 9.40456i −0.777746 0.565065i 0.126556 0.991959i \(-0.459608\pi\)
−0.904302 + 0.426894i \(0.859608\pi\)
\(278\) 1.23607 3.80423i 0.0741344 0.228162i
\(279\) 2.47214 + 7.60845i 0.148003 + 0.455506i
\(280\) 0 0
\(281\) −4.85410 + 3.52671i −0.289571 + 0.210386i −0.723081 0.690763i \(-0.757275\pi\)
0.433510 + 0.901149i \(0.357275\pi\)
\(282\) −1.85410 5.70634i −0.110410 0.339808i
\(283\) −2.47214 + 7.60845i −0.146953 + 0.452276i −0.997257 0.0740167i \(-0.976418\pi\)
0.850304 + 0.526292i \(0.176418\pi\)
\(284\) −4.85410 3.52671i −0.288038 0.209272i
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) −0.809017 0.587785i −0.0476718 0.0346356i
\(289\) 5.87132 18.0701i 0.345372 1.06295i
\(290\) 0 0
\(291\) −11.3262 + 8.22899i −0.663956 + 0.482392i
\(292\) 1.61803 1.17557i 0.0946883 0.0687951i
\(293\) 1.85410 + 5.70634i 0.108318 + 0.333368i 0.990495 0.137550i \(-0.0439228\pi\)
−0.882177 + 0.470918i \(0.843923\pi\)
\(294\) −0.927051 + 2.85317i −0.0540667 + 0.166400i
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −19.4164 14.1068i −1.12288 0.815820i
\(300\) −1.54508 + 4.75528i −0.0892055 + 0.274546i
\(301\) 4.94427 + 15.2169i 0.284983 + 0.877088i
\(302\) −8.09017 + 5.87785i −0.465537 + 0.338232i
\(303\) 4.85410 3.52671i 0.278861 0.202604i
\(304\) 1.23607 + 3.80423i 0.0708934 + 0.218187i
\(305\) 0 0
\(306\) −4.85410 3.52671i −0.277491 0.201609i
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −5.56231 + 17.1190i −0.315409 + 0.970730i 0.660176 + 0.751111i \(0.270482\pi\)
−0.975586 + 0.219620i \(0.929518\pi\)
\(312\) 1.23607 + 3.80423i 0.0699786 + 0.215372i
\(313\) −21.0344 + 15.2824i −1.18894 + 0.863813i −0.993152 0.116834i \(-0.962726\pi\)
−0.195785 + 0.980647i \(0.562726\pi\)
\(314\) −1.61803 + 1.17557i −0.0913109 + 0.0663413i
\(315\) 0 0
\(316\) −4.32624 + 13.3148i −0.243370 + 0.749016i
\(317\) −9.70820 7.05342i −0.545267 0.396160i 0.280770 0.959775i \(-0.409410\pi\)
−0.826037 + 0.563615i \(0.809410\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −9.70820 7.05342i −0.541859 0.393684i
\(322\) −3.70820 + 11.4127i −0.206650 + 0.636004i
\(323\) 7.41641 + 22.8254i 0.412660 + 1.27004i
\(324\) −0.809017 + 0.587785i −0.0449454 + 0.0326547i
\(325\) 16.1803 11.7557i 0.897524 0.652089i
\(326\) −1.23607 3.80423i −0.0684595 0.210697i
\(327\) 1.23607 3.80423i 0.0683547 0.210374i
\(328\) 4.85410 + 3.52671i 0.268023 + 0.194730i
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −9.70820 7.05342i −0.532807 0.387107i
\(333\) −3.09017 + 9.51057i −0.169340 + 0.521176i
\(334\) −3.70820 11.4127i −0.202904 0.624474i
\(335\) 0 0
\(336\) 1.61803 1.17557i 0.0882710 0.0641326i
\(337\) −0.618034 1.90211i −0.0336665 0.103615i 0.932811 0.360366i \(-0.117348\pi\)
−0.966478 + 0.256751i \(0.917348\pi\)
\(338\) 0.927051 2.85317i 0.0504249 0.155192i
\(339\) −14.5623 10.5801i −0.790916 0.574634i
\(340\) 0 0
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) −16.1803 11.7557i −0.873656 0.634748i
\(344\) −2.47214 + 7.60845i −0.133289 + 0.410220i
\(345\) 0 0
\(346\) 4.85410 3.52671i 0.260958 0.189597i
\(347\) 29.1246 21.1603i 1.56349 1.13594i 0.630418 0.776256i \(-0.282883\pi\)
0.933073 0.359687i \(-0.117117\pi\)
\(348\) −1.85410 5.70634i −0.0993903 0.305892i
\(349\) 1.23607 3.80423i 0.0661652 0.203636i −0.912508 0.409059i \(-0.865857\pi\)
0.978673 + 0.205423i \(0.0658571\pi\)
\(350\) −8.09017 5.87785i −0.432438 0.314184i
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.85410 5.70634i −0.0982672 0.302435i
\(357\) 9.70820 7.05342i 0.513813 0.373307i
\(358\) −19.4164 + 14.1068i −1.02619 + 0.745570i
\(359\) 3.70820 + 11.4127i 0.195712 + 0.602338i 0.999968 + 0.00805517i \(0.00256407\pi\)
−0.804256 + 0.594283i \(0.797436\pi\)
\(360\) 0 0
\(361\) 2.42705 + 1.76336i 0.127740 + 0.0928082i
\(362\) −22.0000 −1.15629
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) 0 0
\(366\) −2.47214 + 7.60845i −0.129221 + 0.397700i
\(367\) 2.47214 + 7.60845i 0.129044 + 0.397158i 0.994616 0.103627i \(-0.0330448\pi\)
−0.865572 + 0.500785i \(0.833045\pi\)
\(368\) −4.85410 + 3.52671i −0.253038 + 0.183843i
\(369\) 4.85410 3.52671i 0.252694 0.183593i
\(370\) 0 0
\(371\) 0 0
\(372\) −6.47214 4.70228i −0.335565 0.243802i
\(373\) −20.0000 −1.03556 −0.517780 0.855514i \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.85410 + 3.52671i 0.250331 + 0.181876i
\(377\) −7.41641 + 22.8254i −0.381964 + 1.17557i
\(378\) −0.618034 1.90211i −0.0317882 0.0978341i
\(379\) −16.1803 + 11.7557i −0.831128 + 0.603850i −0.919878 0.392204i \(-0.871713\pi\)
0.0887501 + 0.996054i \(0.471713\pi\)
\(380\) 0 0
\(381\) −4.32624 13.3148i −0.221640 0.682137i
\(382\) 5.56231 17.1190i 0.284592 0.875885i
\(383\) −4.85410 3.52671i −0.248033 0.180207i 0.456822 0.889558i \(-0.348988\pi\)
−0.704855 + 0.709352i \(0.748988\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 6.47214 + 4.70228i 0.328997 + 0.239030i
\(388\) 4.32624 13.3148i 0.219631 0.675956i
\(389\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(390\) 0 0
\(391\) −29.1246 + 21.1603i −1.47289 + 1.07012i
\(392\) −0.927051 2.85317i −0.0468231 0.144107i
\(393\) 3.70820 11.4127i 0.187054 0.575693i
\(394\) 4.85410 + 3.52671i 0.244546 + 0.177673i
\(395\) 0 0
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 3.23607 + 2.35114i 0.162209 + 0.117852i
\(399\) −2.47214 + 7.60845i −0.123762 + 0.380899i
\(400\) −1.54508 4.75528i −0.0772542 0.237764i
\(401\) −24.2705 + 17.6336i −1.21201 + 0.880578i −0.995412 0.0956827i \(-0.969497\pi\)
−0.216600 + 0.976261i \(0.569497\pi\)
\(402\) 3.23607 2.35114i 0.161400 0.117264i
\(403\) 9.88854 + 30.4338i 0.492583 + 1.51602i
\(404\) −1.85410 + 5.70634i −0.0922450 + 0.283901i
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) −27.5066 19.9847i −1.36011 0.988180i −0.998438 0.0558755i \(-0.982205\pi\)
−0.361675 0.932304i \(-0.617795\pi\)
\(410\) 0 0
\(411\) −5.56231 17.1190i −0.274368 0.844419i
\(412\) 3.23607 2.35114i 0.159430 0.115832i
\(413\) 0 0
\(414\) 1.85410 + 5.70634i 0.0911241 + 0.280451i
\(415\) 0 0
\(416\) −3.23607 2.35114i −0.158661 0.115274i
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −3.09017 + 9.51057i −0.150606 + 0.463517i −0.997689 0.0679432i \(-0.978356\pi\)
0.847084 + 0.531460i \(0.178356\pi\)
\(422\) −2.47214 7.60845i −0.120342 0.370374i
\(423\) 4.85410 3.52671i 0.236015 0.171475i
\(424\) 0 0
\(425\) −9.27051 28.5317i −0.449686 1.38399i
\(426\) 1.85410 5.70634i 0.0898315 0.276473i
\(427\) −12.9443 9.40456i −0.626417 0.455119i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 8.03444 + 24.7275i 0.386111 + 1.18833i 0.935671 + 0.352873i \(0.114795\pi\)
−0.549561 + 0.835454i \(0.685205\pi\)
\(434\) 12.9443 9.40456i 0.621345 0.451434i
\(435\) 0 0
\(436\) 1.23607 + 3.80423i 0.0591969 + 0.182189i
\(437\) 7.41641 22.8254i 0.354775 1.09188i
\(438\) 1.61803 + 1.17557i 0.0773127 + 0.0561709i
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) −19.4164 14.1068i −0.923544 0.670994i
\(443\) −7.41641 + 22.8254i −0.352364 + 1.08447i 0.605158 + 0.796105i \(0.293110\pi\)
−0.957522 + 0.288360i \(0.906890\pi\)
\(444\) −3.09017 9.51057i −0.146653 0.451351i
\(445\) 0 0
\(446\) 12.9443 9.40456i 0.612929 0.445319i
\(447\) 1.85410 + 5.70634i 0.0876960 + 0.269901i
\(448\) −0.618034 + 1.90211i −0.0291994 + 0.0898664i
\(449\) −4.85410 3.52671i −0.229079 0.166436i 0.467325 0.884086i \(-0.345218\pi\)
−0.696404 + 0.717650i \(0.745218\pi\)
\(450\) −5.00000 −0.235702
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) −8.09017 5.87785i −0.380109 0.276166i
\(454\) 3.70820 11.4127i 0.174035 0.535624i
\(455\) 0 0
\(456\) −3.23607 + 2.35114i −0.151543 + 0.110102i
\(457\) −8.09017 + 5.87785i −0.378442 + 0.274954i −0.760703 0.649100i \(-0.775146\pi\)
0.382261 + 0.924054i \(0.375146\pi\)
\(458\) −6.79837 20.9232i −0.317667 0.977679i
\(459\) 1.85410 5.70634i 0.0865421 0.266349i
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 4.85410 + 3.52671i 0.225346 + 0.163723i
\(465\) 0 0
\(466\) 5.56231 + 17.1190i 0.257669 + 0.793023i
\(467\) 9.70820 7.05342i 0.449242 0.326393i −0.340054 0.940406i \(-0.610445\pi\)
0.789296 + 0.614012i \(0.210445\pi\)
\(468\) −3.23607 + 2.35114i −0.149587 + 0.108682i
\(469\) 2.47214 + 7.60845i 0.114153 + 0.351326i
\(470\) 0 0
\(471\) −1.61803 1.17557i −0.0745551 0.0541674i
\(472\) 0 0
\(473\) 0 0
\(474\) −14.0000 −0.643041
\(475\) 16.1803 + 11.7557i 0.742405 + 0.539389i
\(476\) −3.70820 + 11.4127i −0.169965 + 0.523099i
\(477\) 0 0
\(478\) −9.70820 + 7.05342i −0.444043 + 0.322616i
\(479\) −19.4164 + 14.1068i −0.887158 + 0.644558i −0.935136 0.354290i \(-0.884723\pi\)
0.0479772 + 0.998848i \(0.484723\pi\)
\(480\) 0 0
\(481\) −12.3607 + 38.0423i −0.563598 + 1.73458i
\(482\) −8.09017 5.87785i −0.368497 0.267729i
\(483\) −12.0000 −0.546019
\(484\) 0 0
\(485\) 0 0
\(486\) −0.809017 0.587785i −0.0366978 0.0266625i
\(487\) 6.18034 19.0211i 0.280058 0.861930i −0.707779 0.706434i \(-0.750303\pi\)
0.987837 0.155495i \(-0.0496974\pi\)
\(488\) −2.47214 7.60845i −0.111908 0.344418i
\(489\) 3.23607 2.35114i 0.146340 0.106322i
\(490\) 0 0
\(491\) −3.70820 11.4127i −0.167349 0.515047i 0.831853 0.554996i \(-0.187280\pi\)
−0.999202 + 0.0399494i \(0.987280\pi\)
\(492\) −1.85410 + 5.70634i −0.0835894 + 0.257262i
\(493\) 29.1246 + 21.1603i 1.31171 + 0.953011i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 9.70820 + 7.05342i 0.435472 + 0.316389i
\(498\) 3.70820 11.4127i 0.166169 0.511414i
\(499\) −1.23607 3.80423i −0.0553340 0.170301i 0.919570 0.392926i \(-0.128537\pi\)
−0.974904 + 0.222626i \(0.928537\pi\)
\(500\) 0 0
\(501\) 9.70820 7.05342i 0.433731 0.315124i
\(502\) 0 0
\(503\) −3.70820 + 11.4127i −0.165341 + 0.508866i −0.999061 0.0433204i \(-0.986206\pi\)
0.833721 + 0.552187i \(0.186206\pi\)
\(504\) 1.61803 + 1.17557i 0.0720730 + 0.0523641i
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 11.3262 + 8.22899i 0.502521 + 0.365103i
\(509\) 7.41641 22.8254i 0.328726 1.01172i −0.641004 0.767538i \(-0.721482\pi\)
0.969730 0.244178i \(-0.0785183\pi\)
\(510\) 0 0
\(511\) −3.23607 + 2.35114i −0.143155 + 0.104008i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 1.23607 + 3.80423i 0.0545737 + 0.167961i
\(514\) −9.27051 + 28.5317i −0.408905 + 1.25848i
\(515\) 0 0
\(516\) −8.00000 −0.352180
\(517\) 0 0
\(518\) 20.0000 0.878750
\(519\) 4.85410 + 3.52671i 0.213071 + 0.154805i
\(520\) 0 0
\(521\) −5.56231 17.1190i −0.243689 0.749998i −0.995849 0.0910175i \(-0.970988\pi\)
0.752160 0.658980i \(-0.229012\pi\)
\(522\) 4.85410 3.52671i 0.212458 0.154360i
\(523\) −12.9443 + 9.40456i −0.566013 + 0.411233i −0.833655 0.552286i \(-0.813756\pi\)
0.267641 + 0.963519i \(0.413756\pi\)
\(524\) 3.70820 + 11.4127i 0.161994 + 0.498565i
\(525\) 3.09017 9.51057i 0.134866 0.415075i
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) −2.47214 7.60845i −0.107181 0.329868i
\(533\) 19.4164 14.1068i 0.841018 0.611035i
\(534\) 4.85410 3.52671i 0.210058 0.152616i
\(535\) 0 0
\(536\) −1.23607 + 3.80423i −0.0533900 + 0.164318i
\(537\) −19.4164 14.1068i −0.837880 0.608755i
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) 16.1803 + 11.7557i 0.695647 + 0.505417i 0.878512 0.477721i \(-0.158537\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(542\) −0.618034 + 1.90211i −0.0265468 + 0.0817028i
\(543\) −6.79837 20.9232i −0.291746 0.897902i
\(544\) −4.85410 + 3.52671i −0.208118 + 0.151207i
\(545\) 0 0
\(546\) −2.47214 7.60845i −0.105798 0.325612i
\(547\) 8.65248 26.6296i 0.369953 1.13860i −0.576868 0.816838i \(-0.695725\pi\)
0.946821 0.321761i \(-0.104275\pi\)
\(548\) 14.5623 + 10.5801i 0.622071 + 0.451961i
\(549\) −8.00000 −0.341432
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) −4.85410 3.52671i −0.206604 0.150107i
\(553\) 8.65248 26.6296i 0.367941 1.13241i
\(554\) 4.94427 + 15.2169i 0.210062 + 0.646504i
\(555\) 0 0
\(556\) −3.23607 + 2.35114i −0.137240 + 0.0997106i
\(557\) −5.56231 17.1190i −0.235682 0.725356i −0.997030 0.0770122i \(-0.975462\pi\)
0.761348 0.648344i \(-0.224538\pi\)
\(558\) 2.47214 7.60845i 0.104654 0.322091i
\(559\) 25.8885 + 18.8091i 1.09497 + 0.795541i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −9.70820 7.05342i −0.409152 0.297266i 0.364106 0.931357i \(-0.381374\pi\)
−0.773258 + 0.634091i \(0.781374\pi\)
\(564\) −1.85410 + 5.70634i −0.0780718 + 0.240280i
\(565\) 0 0
\(566\) 6.47214 4.70228i 0.272044 0.197652i
\(567\) 1.61803 1.17557i 0.0679510 0.0493693i
\(568\) 1.85410 + 5.70634i 0.0777964 + 0.239433i
\(569\) −5.56231 + 17.1190i −0.233184 + 0.717667i 0.764173 + 0.645011i \(0.223147\pi\)
−0.997357 + 0.0726553i \(0.976853\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) −9.70820 7.05342i −0.405213 0.294404i
\(575\) −9.27051 + 28.5317i −0.386607 + 1.18985i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) 27.5066 19.9847i 1.14511 0.831974i 0.157290 0.987552i \(-0.449724\pi\)
0.987824 + 0.155579i \(0.0497242\pi\)
\(578\) −15.3713 + 11.1679i −0.639363 + 0.464524i
\(579\) −4.32624 13.3148i −0.179792 0.553344i
\(580\) 0 0
\(581\) 19.4164 + 14.1068i 0.805528 + 0.585251i
\(582\) 14.0000 0.580319
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 1.85410 5.70634i 0.0765922 0.235727i
\(587\) 7.41641 + 22.8254i 0.306108 + 0.942103i 0.979261 + 0.202601i \(0.0649393\pi\)
−0.673154 + 0.739503i \(0.735061\pi\)
\(588\) 2.42705 1.76336i 0.100090 0.0727196i
\(589\) −25.8885 + 18.8091i −1.06672 + 0.775017i
\(590\) 0 0
\(591\) −1.85410 + 5.70634i −0.0762676 + 0.234727i
\(592\) 8.09017 + 5.87785i 0.332504 + 0.241578i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.85410 3.52671i −0.198832 0.144460i
\(597\) −1.23607 + 3.80423i −0.0505889 + 0.155697i
\(598\) 7.41641 + 22.8254i 0.303279 + 0.933398i
\(599\) −24.2705 + 17.6336i −0.991666 + 0.720488i −0.960285 0.279020i \(-0.909990\pi\)
−0.0313808 + 0.999508i \(0.509990\pi\)
\(600\) 4.04508 2.93893i 0.165140 0.119981i
\(601\) 6.79837 + 20.9232i 0.277311 + 0.853477i 0.988599 + 0.150575i \(0.0481126\pi\)
−0.711287 + 0.702902i \(0.751887\pi\)
\(602\) 4.94427 15.2169i 0.201513 0.620195i
\(603\) 3.23607 + 2.35114i 0.131783 + 0.0957459i
\(604\) 10.0000 0.406894
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) 11.3262 + 8.22899i 0.459718 + 0.334005i 0.793421 0.608674i \(-0.208298\pi\)
−0.333703 + 0.942678i \(0.608298\pi\)
\(608\) 1.23607 3.80423i 0.0501292 0.154282i
\(609\) 3.70820 + 11.4127i 0.150264 + 0.462465i
\(610\) 0 0
\(611\) 19.4164 14.1068i 0.785504 0.570702i
\(612\) 1.85410 + 5.70634i 0.0749476 + 0.230665i
\(613\) 4.94427 15.2169i 0.199697 0.614605i −0.800192 0.599744i \(-0.795269\pi\)
0.999890 0.0148615i \(-0.00473072\pi\)
\(614\) 16.1803 + 11.7557i 0.652985 + 0.474422i
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 3.23607 + 2.35114i 0.130174 + 0.0945768i
\(619\) 13.5967 41.8465i 0.546499 1.68195i −0.170898 0.985289i \(-0.554667\pi\)
0.717398 0.696664i \(-0.245333\pi\)
\(620\) 0 0
\(621\) −4.85410 + 3.52671i −0.194788 + 0.141522i
\(622\) 14.5623 10.5801i 0.583895 0.424225i
\(623\) 3.70820 + 11.4127i 0.148566 + 0.457239i
\(624\) 1.23607 3.80423i 0.0494823 0.152291i
\(625\) −20.2254 14.6946i −0.809017 0.587785i
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 48.5410 + 35.2671i 1.93546 + 1.40619i
\(630\) 0 0
\(631\) −4.94427 15.2169i −0.196828 0.605775i −0.999950 0.00996082i \(-0.996829\pi\)
0.803122 0.595815i \(-0.203171\pi\)
\(632\) 11.3262 8.22899i 0.450534 0.327332i
\(633\) 6.47214 4.70228i 0.257244 0.186899i
\(634\) 3.70820 + 11.4127i 0.147272 + 0.453255i
\(635\) 0 0
\(636\) 0 0
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 1.85410 5.70634i 0.0732326 0.225387i −0.907740 0.419533i \(-0.862194\pi\)
0.980973 + 0.194147i \(0.0621937\pi\)
\(642\) 3.70820 + 11.4127i 0.146351 + 0.450422i
\(643\) 3.23607 2.35114i 0.127618 0.0927200i −0.522145 0.852857i \(-0.674868\pi\)
0.649763 + 0.760137i \(0.274868\pi\)
\(644\) 9.70820 7.05342i 0.382557 0.277944i
\(645\) 0 0
\(646\) 7.41641 22.8254i 0.291795 0.898052i
\(647\) −4.85410 3.52671i −0.190834 0.138649i 0.488266 0.872695i \(-0.337630\pi\)
−0.679100 + 0.734046i \(0.737630\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 12.9443 + 9.40456i 0.507326 + 0.368594i
\(652\) −1.23607 + 3.80423i −0.0484082 + 0.148985i
\(653\) −11.1246 34.2380i −0.435340 1.33984i −0.892738 0.450576i \(-0.851219\pi\)
0.457398 0.889262i \(-0.348781\pi\)
\(654\) −3.23607 + 2.35114i −0.126540 + 0.0919369i
\(655\) 0 0
\(656\) −1.85410 5.70634i −0.0723905 0.222795i
\(657\) −0.618034 + 1.90211i −0.0241118 + 0.0742085i
\(658\) −9.70820 7.05342i −0.378465 0.274971i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 3.23607 + 2.35114i 0.125773 + 0.0913797i
\(663\) 7.41641 22.8254i 0.288029 0.886463i
\(664\) 3.70820 + 11.4127i 0.143906 + 0.442898i
\(665\) 0 0
\(666\) 8.09017 5.87785i 0.313488 0.227762i
\(667\) −11.1246 34.2380i −0.430747 1.32570i
\(668\) −3.70820 + 11.4127i −0.143475 + 0.441570i
\(669\) 12.9443 + 9.40456i 0.500454 + 0.363601i
\(670\) 0 0
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) 11.3262 + 8.22899i 0.436594 + 0.317204i 0.784280 0.620407i \(-0.213032\pi\)
−0.347686 + 0.937611i \(0.613032\pi\)
\(674\) −0.618034 + 1.90211i −0.0238058 + 0.0732667i
\(675\) −1.54508 4.75528i −0.0594703 0.183031i
\(676\) −2.42705 + 1.76336i −0.0933481 + 0.0678214i
\(677\) 24.2705 17.6336i 0.932791 0.677713i −0.0138832 0.999904i \(-0.504419\pi\)
0.946675 + 0.322191i \(0.104419\pi\)
\(678\) 5.56231 + 17.1190i 0.213619 + 0.657452i
\(679\) −8.65248 + 26.6296i −0.332052 + 1.02195i
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −3.23607 2.35114i −0.123734 0.0898981i
\(685\) 0 0
\(686\) 6.18034 + 19.0211i 0.235966 + 0.726230i
\(687\) 17.7984 12.9313i 0.679050 0.493359i
\(688\) 6.47214 4.70228i 0.246748 0.179273i
\(689\) 0 0
\(690\) 0 0
\(691\) −16.1803 11.7557i −0.615529 0.447208i 0.235828 0.971795i \(-0.424220\pi\)
−0.851357 + 0.524587i \(0.824220\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) −1.85410 + 5.70634i −0.0702796 + 0.216298i
\(697\) −11.1246 34.2380i −0.421375 1.29686i
\(698\) −3.23607 + 2.35114i −0.122487 + 0.0889920i
\(699\) −14.5623 + 10.5801i −0.550797 + 0.400177i
\(700\) 3.09017 + 9.51057i 0.116797 + 0.359466i
\(701\) 1.85410 5.70634i 0.0700285 0.215525i −0.909917 0.414790i \(-0.863855\pi\)
0.979946 + 0.199264i \(0.0638552\pi\)
\(702\) −3.23607 2.35114i −0.122138 0.0887381i
\(703\) −40.0000 −1.50863
\(704\) 0 0
\(705\) 0 0
\(706\) 4.85410 + 3.52671i 0.182687 + 0.132730i
\(707\) 3.70820 11.4127i 0.139461 0.429218i
\(708\) 0 0
\(709\) −21.0344 + 15.2824i −0.789965 + 0.573943i −0.907953 0.419072i \(-0.862356\pi\)
0.117988 + 0.993015i \(0.462356\pi\)
\(710\) 0 0
\(711\) −4.32624 13.3148i −0.162247 0.499344i
\(712\) −1.85410 + 5.70634i −0.0694854 + 0.213854i
\(713\) −38.8328 28.2137i −1.45430 1.05661i
\(714\) −12.0000 −0.449089
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −9.70820 7.05342i −0.362560 0.263415i
\(718\) 3.70820 11.4127i 0.138389 0.425917i
\(719\) 9.27051 + 28.5317i 0.345732 + 1.06405i 0.961191 + 0.275884i \(0.0889706\pi\)
−0.615459 + 0.788169i \(0.711029\pi\)
\(720\) 0 0
\(721\) −6.47214 + 4.70228i −0.241035 + 0.175122i
\(722\) −0.927051 2.85317i −0.0345013 0.106184i
\(723\) 3.09017 9.51057i 0.114925 0.353702i
\(724\) 17.7984 + 12.9313i 0.661471 + 0.480587i
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 6.47214 + 4.70228i 0.239873 + 0.174278i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) 38.8328 28.2137i 1.43628 1.04352i
\(732\) 6.47214 4.70228i 0.239217 0.173801i
\(733\) 1.23607 + 3.80423i 0.0456552 + 0.140512i 0.971286 0.237917i \(-0.0764645\pi\)
−0.925630 + 0.378429i \(0.876464\pi\)
\(734\) 2.47214 7.60845i 0.0912482 0.280833i
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) 6.47214 + 4.70228i 0.238081 + 0.172976i 0.700428 0.713723i \(-0.252992\pi\)
−0.462347 + 0.886699i \(0.652992\pi\)
\(740\) 0 0
\(741\) 4.94427 + 15.2169i 0.181632 + 0.559007i
\(742\) 0 0
\(743\) 29.1246 21.1603i 1.06848 0.776295i 0.0928402 0.995681i \(-0.470405\pi\)
0.975638 + 0.219386i \(0.0704054\pi\)
\(744\) 2.47214 + 7.60845i 0.0906329 + 0.278939i
\(745\) 0 0
\(746\) 16.1803 + 11.7557i 0.592404 + 0.430407i
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 2.47214 7.60845i 0.0902095 0.277636i −0.895766 0.444526i \(-0.853372\pi\)
0.985976 + 0.166889i \(0.0533723\pi\)
\(752\) −1.85410 5.70634i −0.0676121 0.208089i
\(753\) 0 0
\(754\) 19.4164 14.1068i 0.707104 0.513741i
\(755\) 0 0
\(756\) −0.618034 + 1.90211i −0.0224777 + 0.0691792i
\(757\) 27.5066 + 19.9847i 0.999744 + 0.726356i 0.962033 0.272932i \(-0.0879936\pi\)
0.0377104 + 0.999289i \(0.487994\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) 14.5623 + 10.5801i 0.527883 + 0.383530i 0.819565 0.572986i \(-0.194215\pi\)
−0.291682 + 0.956515i \(0.594215\pi\)
\(762\) −4.32624 + 13.3148i −0.156723 + 0.482344i
\(763\) −2.47214 7.60845i −0.0894973 0.275444i
\(764\) −14.5623 + 10.5801i −0.526846 + 0.382776i
\(765\) 0 0
\(766\) 1.85410 + 5.70634i 0.0669914 + 0.206178i
\(767\) 0 0
\(768\) −0.809017 0.587785i −0.0291929 0.0212099i
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) 11.3262 + 8.22899i 0.407640 + 0.296168i
\(773\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(774\) −2.47214 7.60845i −0.0888591 0.273480i
\(775\) 32.3607 23.5114i 1.16243 0.844555i
\(776\) −11.3262 + 8.22899i −0.406588 + 0.295404i
\(777\) 6.18034 + 19.0211i 0.221718 + 0.682379i
\(778\) 0 0
\(779\) 19.4164 + 14.1068i 0.695665 + 0.505430i
\(780\) 0 0
\(781\) 0 0
\(782\) 36.0000 1.28736
\(783\) 4.85410 + 3.52671i 0.173471 + 0.126034i
\(784\) −0.927051 + 2.85317i −0.0331090 + 0.101899i